Method and apparatus for the calculation of coal ash fusion values

ABSTRACT

The IT and FT values for coal and coke samples can be accurately predicted by applying equations to determined ST and HT temperatures. For reducing atmospheres, the equations are IT=C 1 ×ST−C 2 ×HT+C 3  and FT=C 4 ×HT−C 5 ×ST+C 6 . For oxidizing atmospheres, the equations are IT=C 7 ×ST−C 8 ×HT+C 9  and FT=C 10 ×HT−C 11 ×ST+C 12 . IT is the initial deformation temperature. ST is the softening temperature. HT is the hemispherical temperature. FT is the fluid temperature. C 1 -C 12  are constants determined by multi-linear regression coefficient analytical techniques on a collection of data.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.11/937,566, filed on Nov. 9, 2007, entitled METHOD AND APPARATUS FOR THECALCULATION OF COAL ASH FUSION VALUES, the entire disclosures of whichare incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention is a method and apparatus for the calculation ofcoal ash fusion values based upon the measurement of predetermined ashfusion values.

The efficient operation of coal-fired power plant boilers and otherboilers and furnaces with a minimum of slagging and fouling problemsdepends on the determination of accurate ash fusion temperatures for thecoals used as fuels. Such industrial combustion equipment may remove thebyproducts of the combustion process in either a solid or liquid formdepending on equipment type. It is imperative that the coal utilizedmaintain appropriate ash properties during the entire handling process.Ash fusion temperatures are a useful guide to a coal's expectedbehavior.

Before coal or coke is burned in a furnace, the fuel is analyzed todetermine the fusibility of the coal or coke ash. Burning coal or cokein a commercial steel mill furnace, which generates temperaturessufficiently high to fuse the ash, causes the ash to collect on variousfurnace components, most notably the furnace grates. If collectionbecomes excessive, the furnace must be shut down, cooled, and cleaned,requiring costly excessive periods of furnace inactivity. By selectingcoal with desired properties, such problems can be minimized.

The ASTM standard test method for determining the fusibility of coal andcoke ash requires the prepared ash to be formed into triangular,generally pyramid-shaped cones which are placed within an analyticalfurnace. The temperature within the furnace is then increasingly rampedat 15° F. per minute, and the cones are manually observed to detectchanges in shape. The fusibility of the ash is recorded at fourtemperatures; namely, (1) the temperature at which the apex of the conebecomes rounded known as initial deformation temperature (IDT,hereinafter abbreviated as IT); (2) the temperature at which the heightof the deformed cone is equal to the width of the base known as thesoftening temperature (ST); (3) the temperature at which the height ofthe deformed cone is equal to one-half the width of the base known asthe hemispherical temperature (HT); and, finally, (4) the temperature atwhich the cone has been reduced to a lump having a height no greaterthan one-sixteenth inch known as the fluid temperature (FT).

This test method has several significant drawbacks. First the method istime-consuming and requires an observer to constantly monitor all coneswithin the furnace as all cones pass through all four stages of fusion.This task is tedious and the observer can become inattentive, resultingin inaccurate temperature readings. Second, monitoring the shape of fivecones (the typical furnace load) is difficult. Third, the findings aresomewhat subject to the individual judgment of the human observer,further introducing error and/or variation into the test results. TheASTM test method recognizes these problems and provides for relativelylarge acceptable errors in excess of 50° C. or 100° F. for each of thefour stages of fusion.

Improvements in ash fusion determinators have greatly improved theaccuracy of the determination of IT, ST, HT, and FT. An ash fusiondeterminator Model No. AF700, commercially available from LecoCorporation of St. Joseph, Mich., represents state-of-the-art advancesover several earlier determinators, such as disclosed in U.S. Pat. Nos.4,462,963 and 4,522,787. The AF700 ash fusibility determinatorautomatically monitors ash cone deformation temperatures in coal ash,coke ash, and mold powders. Prepared ash cones are mounted on a ceramictray and placed into a high-temperature, rampable furnace. The userselects an analytical method with a predefined furnace atmosphere(oxidizing or reducing) and a ramp rate (° C./minute) for the furnacebased on approved methodologies. The furnace is first purged withnitrogen before the selected atmosphere is introduced. A high-resolutiondigital camera collects images (up to 30 frames/minute) after thefurnace temperature reaches the method-defined starting point (typically1382° F./750° C.). Predefined ash fusibility temperatures (IT, ST, HT,and FT) may be automatically determined using Image RecognitionFunctions (IRF) within the software. In addition, IRF allows theanalysis to be automatically terminated after all deformation pointshave been reached for all samples, increasing throughput and furnacelifetime. Alternately, the furnace can be programmed to cycle betweenthe method-defined starting temperature (e.g. 752° F./400° C.) and amaximum programmed furnace temperature (typically 2730° F./1500° C. anda maximum of 2900° F./1600° C.). A complete image history for allanalyzed samples is digitally archived for easy retrieval and review onDVD, CDRW, or hard drive. Archived images may be used to make subjectivedeterminations of deformation temperatures.

Although such a determinator has greatly improved the efficiency of thedetermination of the ash fusion temperature, subjective, somewhaterror-prone steps, are still required. Although the softeningtemperature (ST) and hemispherical temperature (HT) phases are welldefined in mathematical terms, the initial deformation temperature (IDTor IT) and the fluid temperature (FT) phases remain subjectiveobservations and are much more difficult to accurately determine. Thus,there remains a need for improvement in the accurate determination ofthe ASTM ash fusion temperatures.

SUMMARY OF THE INVENTION

It has been discovered through extensive testing of coal and cokematerials at numerous laboratories utilizing several samples that analgorithm for predicting the IT and FT based upon measured ST and HTtemperatures results in more accurate determination of these endpointtemperatures than the actual subjective determination of them. Utilizingmulti-linear regression coefficient analytical techniques, the followingequations were developed utilizing the empirically gathered data:

For reducing atmospheres:

IT=C ₁ ×ST−C ₂ ×HT+C ₃

FT=C ₄ ×HT−C ₅ ×ST+C ₆

For oxidizing atmospheres:

IT=C ₇ ×ST−C ₈ ×HT+C ₉

FT=C ₁₀ ×HT−C ₁₁ ×ST+C ₁₂

-   -   Where:        -   IT is the initial deformation temperature;        -   ST is the softening temperature;        -   HT is the hemispherical temperature;        -   FT is the fluid temperature; and

C₁-C₁₂ are constants determined by multi-linear regression coefficientanalytical techniques on the collection of data.

In a preferred embodiment, the constants C₁-C₁₂ were about (alltemperatures are in ° C.):

C₁=1.56 C₄=1.87 C₇=1.50 C₁₀=1.81 C₂=0.67 C₅=0.96 C₈=0.57 C₁₁=0.89C₃=117.71 C₆=126.79 C₉=77.32 C₁₂=122.29

In a most preferred embodiment, the constants C₁-C₁₂ were (alltemperatures are in ° C.):

C₁=1.5627 C₄=1.8744 C₇=1.5016 C₁₀=1.8131 C₂=0.6684 C₅=0.9568 C₈=0.5724C₁₁=0.8940 C₃=117.7088 C₆=126.7877 C₉=77.3248 C₁₂=122.2880

When Fahrenheit degrees are employed, C₃=215.259; C₆=230.856;C₉=130.665; and C₁₂=223.750. All other constants remain the same. Withthe system and method of the present invention, therefore, an operatorof a commercial coal-burning furnace can accurately and relativelyquickly determine all of the ash fusion temperatures necessary for theefficient operation of the furnace without the need for extensive andtime-consuming burning of coal samples through the FT stage since onlythe ST and HT stages need to be determined by the ash fusion analyzer.

These and other features, objects and advantages of the presentinvention will become apparent upon reading the following descriptionthereof together with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow diagram showing the process by which the algorithm isdeveloped for calculating the IT and FT temperatures based upon measuredHT and ST temperatures;

FIG. 2 is a table of one set of collected data for reducing atmospheresfor numerous samples determining the IT and FT temperature;

FIG. 3 is a table of one set of collected data on numerous samples runin oxidizing atmospheres determining the IT and FT temperatures;

FIG. 4 is a set of equations developed empirically from the multi-linearregression process shown in FIG. 1 and collected data, such as shown inFIGS. 2 and 3; and

FIG. 5 is a flow diagram of the application of the algorithm to measuredHT and ST to determine IT and FT.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

It has been discovered through extensive testing of coal and cokematerials at numerous laboratories utilizing several samples, such asillustrated by the exemplary data shown in FIGS. 2 and 3, that the useof an algorithm for predicting the IT and FT is more accurate than theactual subjective determination of these temperatures utilizing an ashfusion instrument. The data, such as represented in FIGS. 2 and 3, isentered in a computer as indicated by block 10 in FIG. 1. It isunderstood that data from hundreds of samples was used to develop theash fusion equations of FIG. 4, and the data of FIGS. 2 and 3 is asampling of such collected data. As shown by block 12, utilizingconventional multi-linear correlation programs, the IT and FT can becalculated from known IT, HT, ST, and FT data actually determined frommeasurements, as shown by the examples in the tables of FIGS. 2 and 3.The tables of FIGS. 2 and 3 represent one lab's analysis of multiplesamples in reducing and oxidizing atmospheres respectively, it beingunderstood that the training set data entered in block 10 of FIG. 1 isdata from over 20 such labs, each of which independently analyzed over35 coal and coke ash samples to obtain a universe of data whichaccurately reflects the characteristics of coal and coke samples.Predicted initial deformation IT and fluid FT temperatures using thedeveloped ash fusion equations of FIG. 4. differ from the measuredvalues by an average of 7.51° C. to 16.2° C. These are values much lessthan the normal errors experienced in determining these two fusiontemperatures. By comparison, the average “within lab” errors reported inthe measurement of the initial deformation and fluid temperatures of acoal ash ranged from 13.9° C. to 32.9° C.

Utilizing conventional multi-linear regression coefficient analyticaltechniques, as shown by the process of block 14 in FIG. 1, the ashfusion equations of FIG. 4 were determined utilizing the empiricallygathered data (such as shown in FIGS. 2 and 3). The mathematicalanalysis is also known as the least square method for developingequations to fit data to a plot. One discussion of this time honoredtechnique is discussed in an article entitled “Least Squares.” by HervéAbdi, published in Lewis-Beck M., Bryman, A., Futing T. (Eds.) (2003)Encyclopedia of Social Sciences Research Methods, Thousand Oaks (CA),the disclosure of which is incorporated herein by reference. Using thismathematical analysis of the collected data, the series of equationsdeveloped for predicting the initial deformation and fluid temperatureswere determined and are set forth in FIG. 4. (All temperatures are inC.) If Fahrenheit degrees are employed, the constants C₃, C₆, C₉, andC₁₂ change as seen in FIG. 4.

When it is desired to determine the ash fusion parameters IT, ST, HT,and FT of a sample for use in coal fired furnaces, as shown in FIG. 5,the first step 16 is to utilize an ash fusion instrument, such as anAF700 available from Leco Corporation of St. Joseph, Mich., fordetermining only the ST and HT temperatures which, as discussed above,can accurately be determined utilizing existing ash fusion analyzers.

Next, as indicated by block 18 of FIG. 5, employing the data determinedfrom the ash fusion analyzer for ST and HT and utilizing the equationsof FIG. 4, an algorithm, programmed into a computer associated with theash fusion analyzer executes the equations of FIG. 4, to determine thepredicted IT and FT from the accurately measured ST and HT.Subsequently, the output information from the computer is supplied to amonitor, printer, or other output device, as shown by block 20, todisplay both the measured ST and HT from the ash fusion analyzer, aswell as the predicted IT and FT based upon application of the formulasof FIG. 4. The output can be in other usable electronic formats.

With the system and method of the present invention, therefore, anoperator of a commercial coal-burning furnace can accurately andrelatively quickly determine all of the ash fusion temperaturesnecessary for the efficient operation of the furnace without the needfor extensive and time-consuming burning of coal samples through the FTstage since only the ST and HT stages need to be determined by the ashfusion analyzer. Additionally, the exact shape of the specimen beinganalyzed need not be a conventional cone-shape inasmuch as the ST and HTgeometric configurations are well defined and can be determined from ageometric shape other than the classic pyramidal shape of the ASTMstandard. Thus, the analytical process described herein is independentof the choice of shape or quality of the sample block employed for theanalysis.

It will become apparent to those skilled in the art that variousmodifications to the preferred embodiment of the invention, includingmodifications of the mathematical formulas, as described herein can bemade without departing from the spirit or scope of the invention asdefined by the appended claims.

1. A method of predicting IT and FT values from measured ST and HTtemperatures of a specimen by applying a multi-linear regressionanalysis to measured ST and HT temperatures, wherein IT and FT valuesfrom measured ST and HT temperatures of a specimen are computed by acomputer programmed to apply the following formulae:For reducing atmospheres:IT=C ₁ ×ST−C ₂ ×HT+C ₃FT=C ₄ ×HT−C ₅ ×ST+C ₆For oxidizing atmospheres:IT=C ₇ ×ST−C ₈ ×HT+C ₉FT=C ₁₀ ×HT−C ₁₁ ×ST+C ₁₂ Where: IT is the initial deformationtemperature; ST is the softening temperature; HT is the hemisphericaltemperature; FT is the fluid temperature; and C₁-C₁₂ are constantsdetermined by multi-linear regression coefficient analytical techniqueson the collection of data.
 2. The method of claim 1 where C₁ is about1.56, C₂ is about 0.67, C₃ is about 117.71, C₄ is about 1.87, C₅ isabout 0.96, C₆ is about 126.79, C₇ is about 1.50, C₈ is about 0.57, C₉is about 77.32, C₁₀ is about 1.81, C₁₁ is about 0.89, and C₁₂ is about122.29 and where the measured temperatures are in ° C.
 3. The method ofclaim 1 where C₁ is 1.5627, C₂ is about 0.6684, C₃ is about 117.7088, C₄is about 1.8744, C₅ is about 0.9568, C₆ is about 126.7877, C₇ is about1.5016, C₈ is about 0.5724, C₉ is about 77.3248, C₁₀ is about 1.8131,C₁₁ is about 0.8940, and C₁₂ is about 122.2880 and where the measuredtemperatures are in ° C.
 4. The method of claim 1 where C₁ is 1.5627, C₂is about 0.6684, C₃ is about 125.259, C₄ is about 1.8744, C₅ is about0.9568, C₆ is about 230.856, C₇ is about 1.5016, C₈ is about 0.5724, C₉is about 130.665, C₁₀ is about 1.8131, C₁₁ is about 0.8940, and C₁₂ isabout 223.750 and where the measured temperatures are in ° F.
 5. Asystem for the determination of IT, ST, HT, and FT temperatures of aspecimen comprising: an ash fusion analyzer for the determination of STand HT temperatures; a computer coupled to said ash fusion analyzer forreceiving the ST and HT information therefrom and programmed forperforming a multi-linear regression analysis on the ST and HTinformation for calculating the IT and FT temperatures, wherein saidcomputer is programmed for calculating the IT and FT temperatures basedupon the following equations:For reducing atmospheres:IT=C ₁ ×ST−C ₂ ×HT+C ₃FT=C ₄ ×HT−C ₅ ×ST+C ₆For oxidizing atmospheres:IT=C ₇ ×ST−C ₈ ×HT+C ₉FT=C ₁₀ ×HT−C ₁₁ ×ST+C ₁₂ Where: IT is the initial deformationtemperature; ST is the softening temperature; HT is the hemisphericaltemperature; FT is the fluid temperature; and C₁-C₁₂ are constantsdetermined by multi-linear regression coefficient analytical techniqueson the collection of data.
 6. The system as defined in claim 5 where C₁is about 1.56, C₂ is about 0.67, C₃ is about 117.71, C₄ is about 1.87,CS is about 0.96, C₆ is about 126.79, C₇ is about 1.50, C₈ is about0.57, C₉ is about 77.32, C₁₀ is about 1.81, C₁₁ is about 0.89, and C₁₂is about 122.29 and where the measured temperatures are in ° C.
 7. Thesystem as defined in claim 5 where C₁ is 1.5627, C₂ is about 0.6684, C₃is about 117.7088, C₄ is about 1.8744, C₅ is about 0.9568, C₆ is about126.7877, C₇ is about 1.5016, C₈ is about 0.5724, C₉ is about 77.3248,C₁₀ is about 1.8131, C₁₁ is about 0.8940, and C₁₂ is about 122.2880 andwhere the measured temperatures are in ° C.
 8. The system as defined inclaim 5 where C₁ is 1.5627, C₂ is about 0.6684, C₃ is about 215.259, C₄is about 1.8744, CS is about 0.9568, C₆ is about 230.856, C₇ is about1.5016, C₈ is about 0.5724, C₉ is about 130.665, C₁₀ is about 1.8131,C₁₁ is about 0.8940, and C₁₂ is about 223.750 and where the measuredtemperatures are in ° F.
 9. The system as defined in claim 5 whereinsaid system includes an output for the values of IT and FT.
 10. Thesystem as defined in claim 9 wherein said output is a display.
 11. Thesystem as defined in claim 9 wherein said output is a printer
 12. Asystem for the determination of IT, ST, HT, and FT temperatures of aspecimen comprising: a computer for receiving ST and HT data from an ashsample said computer programmed for calculating IT and FT from suchinformation by applying the following equations: For reducingatmospheres:IT=C ₁ ×ST−C ₂ ×HT+C ₃FT=C ₄ ×HT−C ₅ ×ST+C ₆ For oxidizing atmospheres:IT=C ₇ ×ST−C ₈ ×HT+C ₉FT=C ₁₀ ×HT−C ₁₁ ×ST+C ₁₂ Where:IT is the initial deformationtemperature; ST is the softening temperature; HT is the hemisphericaltemperature; FT is the fluid temperature; and C₁-C₁₂ are constantsdetermined by multi-linear regression coefficient analytical techniqueson the collection of data.
 13. The system as defined in claim 12 whereC₁ is about 1.56, C₂ is about 0.67, C₃ is about 117.71, C₄ is about1.87, C₅ is about 0.96, C₆ is about 126.79, C₇ is about 1.50, C₈ isabout 0.57, C₉ is about 77.32, C₁₀ is about 1.81, C₁₁ is about 0.89, andC₁₂ is about 122.29 and where the measured temperatures are in ° C. 14.The system as defined in claim 12 where C₁ is 1.5627, C₂ is about0.6684, C₃ is about 117.7088, C₄ is about 1.8744, C₅ is about 0.9568, C₆is about 126.7877, C₇ is about 1.5016, C₈ is about 0.5724, C₉ is about77.3248, C₁₀ is about 1.8131, C₁₁ is about 0.8940, and C₁₂ is about122.2880 and where the measured temperatures are in ° C.
 15. The systemas defined in claim 12 where C₁ is 1.5627, C₂ is about 0.6684, C₃ isabout 215.259, C₄ is about 1.8744, C₅ is about 0.9568, C₆ is about230.856, C₇ is about 1.5016, C₈ is about 0.5724, C₉ is about 130.665,C₁₀ is about 1.8131, C₁₁ is about 0.8940, and C₁₂ is about 223.750 andwhere the measured temperatures are in ° F.
 16. The system as defined inclaim 13 wherein said system includes an output for the values of IT andFT.
 17. The system as defined in claim 16 wherein said output is adisplay.
 18. The system as defined in claim 17 wherein said output is aprinter.